Question

What is the function rule for g?

Answer 1

Answer:

$g(x)=8(2^x)$

Step-by-step explanation:

Here we are given with parent function $f(x)=2^x$ and the graph which shows that the function g(x).

We are asked to guess the function g(x).

We are given the two coordinates on g(x)

(0,8) and (2,32)

Hence for x = 0 , g(x)= 8

And for x=2, g(x)= 32

Let us say that the translated function is represented by

$g(x)=a2^x+b$

$g(0)=a\times 2^0+b$

Hence

$a \times 2^0+b=8$

$a +b=8$ --------------- (i)

also

$g(2)=32$

Hence

$a\times 2^2+b=32$

$4a+b=32$ -------------------(ii)

Subtracting (i) from (ii) we get

$3a=34$

Hence a = 8

Now putting this value of a in (i)

$8+b=8$

B=0

Hence $g(x)=8 \times 2^x +0$

$g(x)=8(2^x)$